34. Wave Optics

A diffraction grating with $500\text{lines}/\mathrm{mm}$ is illuminated by two wavelengths of light: $450\mathrm{nm}$ and $600\mathrm{nm}.$ What is the distance between the $m=2$ bright fringes of the two colors of light on a screen $1.3\mathrm{m}$ away?

A diffraction grating has $500\text{lines}/\mathrm{mm}.$ If it is illuminated by a laser at $532\mathrm{nm},$ how many bright spots will be observed on a screen placed behind the grating?

A particular kind of oil with an index of refraction of $1.46$ has spilled on water. The different thicknesses of the oil slick result in different colors being strongly reflected at different parts of the spill. But near the edges, you identify the thinnest part of the oil layer that strongly reflects green light with a wavelength of 550 nm when you are directly overhead. What is the thickness of the oil at this point? Assume light is incident normal to the oil surface.

You place one glass slide on top of another, with an animal hair between them at one end. You illuminate the slides with blue light of wavelength $450\mathrm{nm}.$ You count along the slide and find 300 transitions from bright to dark and back to light. How thick is the hair?

b. Use your expression from part a to find an expression for the separation Δy on the screen of two fringes that differ in wavelength by Δλ.

FIGURE EX33.17 shows the interference pattern on a screen 1.0 m behind an 800 lines/mm diffraction grating. What is the wavelength (in nm) of the light?

If the planes of a crystal are 3.50 Å (1 Å = 10-10 m = 1 Ångstrom unit) apart, (a) what wavelength of electromagnetic waves is needed so that the first strong interference maximum in the Bragg reflection occurs when the waves strike the planes at an angle of 22.0°, and in what part of the electromagnetic spectrum do these waves lie?